The maximum degree of hierarchical structure of organisms has risen over the history of life, notably in three transitions: the origin of the eukaryotic cell from symbiotic associations of prokaryotes; the emergence of the first multicellular individuals from clones of eukaryotic cells; and the origin of the first individuated colonies from associations of multicellular organisms. The trend is obvious in the fossil record, but documenting it using a high-resolution hierarchy scale reveals three puzzles: 1) the rate of origin of new levels accelerates, at least until the early Phanerozoic; 2) after that, the trend may slow or even stop; and 3) levels may sometimes arise out of order. The three puzzles and their implications are discussed; a possible explanation is offered for the first.